Any real number line ranges from negative infinity to positive infinity. A real number number line consists of all the rational and irrational numbers. Let us take three intervals which contain both the rational and irrational numbers.
First interval: [3,4]
Since every integer is a rational number, 3 and 4 are both rational. In this interval there occurs the value of π (3.14159..) which is an irrational number.
Second interval : [0,2]
0 and 2 are integers and hence are rational. In this interval, occurs √2 (1.41421...) is an irrational number.
Third interval : [2,3]
In this interval, Eulers number 'e' lie whose value is (2.718281.. )
Hence we can conclude that, there occurs an irrational number between any two rational number.
D should be the correct answer
Answer:
3^9x=3^-2x
Step-by-step explanation:
27^3x=(1/9)^x
3^3×3x=(1/3^2)^x
3^9x=3^-2x
You have 8 people, you have 2 groups of 4.
8!/4!4!
=(8*7*6*5*4*3*2)/(4*3*2*4*3*2)
=(8*7*6*5)/(4*3*2)
=7*6*5/3
=7*2*5
=70
It's been a few years since I've done this. If you haven't learned how to do this type of an equation yet, then I'm probably wrong.
Answer:
<em>The fraction of the beads that are red is</em>
Step-by-step explanation:
<u>Algebraic Expressions</u>
A bag contains red (r), yellow (y), and blue (b) beads. We are given the following ratios:
r:y = 2:3
y:b = 5:4
We are required to find r:s, where s is the total of beads in the bag, or
s = r + y + b
Thus, we need to calculate:
![\displaystyle \frac{r}{r+y+b} \qquad\qquad [1]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Br%2By%2Bb%7D%20%20%20%20%20%20%20%5Cqquad%5Cqquad%20%20%20%20%5B1%5D)
Knowing that:
![\displaystyle \frac{r}{y}=\frac{2}{3} \qquad\qquad [2]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7By%7D%3D%5Cfrac%7B2%7D%7B3%7D%20%20%20%20%20%20%5Cqquad%5Cqquad%20%20%20%20%5B2%5D)
Multiplying the equations above:
Simplifying:
![\displaystyle \frac{r}{b}=\frac{5}{6} \qquad\qquad [3]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Br%7D%7Bb%7D%3D%5Cfrac%7B5%7D%7B6%7D%20%20%20%20%20%20%20%5Cqquad%5Cqquad%20%20%20%20%5B3%5D)
Dividing [1] by r:
Substituting from [2] and [3]:
Operating:
The fraction of the beads that are red is 
